# Magnetic field in materials

1. Jun 1, 2005

### hotel

Hi
I am trying to derive the relation between magnetic field strength in materials and magnetizing field from the $$\mathbf B$$ field. More exactly, my question is:

how do we get this expression

$$\nabla \centerdot \mathbf H = - \nabla \centerdot \mathbf M \\$$

knowing

$$\nabla \centerdot \mathbf B = 0 \\$$

and

$$\mathbf B=\mu_0(\mathbf H + \mathbf M )$$
?

Anyone can guid me how the first equation is related to the 2nd and 3rd equations?

thanku

2. Jun 1, 2005

### inha

$$\nabla \cdot B=\nabla \cdot {\mu}_0(H+M)=0$$

Do you get the idea now?

3. Jun 1, 2005

### hotel

I 'm not sure !?

but how do we get from this:

4. Jun 1, 2005

### inha

$$\nabla \cdot {\mu}_0(H+M)=0$$

divide $$\mu_o$$ out. you can do that since it's just a constant. then you have

$$\nabla \cdot H + \nabla \cdot M=0$$

which is what you're looking for once you move the M-term to the other side of the eq.